public static bool IsOutside(AABB left, AABB right)
{
return (left.MaxX - right.MinX) < 0 || (left.MinX - right.MaxX) > 0 ||
(left.MaxY - right.MinY) < 0 || (left.MinY - right.MaxY) > 0 ||
(left.MaxZ - right.MinZ) < 0 || (left.MinZ - right.MaxZ) > 0
;
}
public CSGMesh(Plane[] planes, List<Polygon> polygons, List<HalfEdge> edges, List<Vector3> vertices, AABB bounds)
{
this.Planes = planes;
this.Polygons = polygons;
this.Edges = edges;
this.Vertices = vertices;
this.Bounds.Set(bounds);
}
public static bool IsOutside(AABB left, Vector3 translation, AABB right)
{
return ((left.MaxX + translation.X) - right.MinX) < 0 || ((left.MinX + translation.X) - right.MaxX) > 0 ||
((left.MaxY + translation.Y) - right.MinY) < 0 || ((left.MinY + translation.Y) - right.MaxY) > 0 ||
((left.MaxZ + translation.Z) - right.MinZ) < 0 || ((left.MinZ + translation.Z) - right.MaxZ) > 0
;
}
public AABB(AABB other)
{
Clear();
Set(other);
}
public void Set(AABB other, Vector3 translation)
{
this.MinX = (int)Math.Floor(other.MinX + translation.X);
this.MinY = (int)Math.Floor(other.MinY + translation.Y);
this.MinZ = (int)Math.Floor(other.MinZ + translation.Z);
this.MaxX = (int)Math.Ceiling(other.MaxX + translation.X);
this.MaxY = (int)Math.Ceiling(other.MaxY + translation.Y);
this.MaxZ = (int)Math.Ceiling(other.MaxZ + translation.Z);
}
public void Set(AABB bounds)
{
this.MinX = bounds.MinX;
this.MinY = bounds.MinY;
this.MinZ = bounds.MinZ;
this.MaxX = bounds.MaxX;
this.MaxY = bounds.MaxY;
this.MaxZ = bounds.MaxZ;
}
public bool IsOutside(AABB other)
{
return (this.MaxX - other.MinX) < 0 || (this.MinX - other.MaxX) > 0 ||
(this.MaxY - other.MinY) < 0 || (this.MinY - other.MaxY) > 0 ||
(this.MaxZ - other.MinZ) < 0 || (this.MinZ - other.MaxZ) > 0
;
}
public void Add(AABB bounds)
{
MinX = Math.Min(MinX, bounds.MinX);
MinY = Math.Min(MinY, bounds.MinY);
MinZ = Math.Min(MinZ, bounds.MinZ);
MaxX = Math.Max(MaxX, bounds.MaxX);
MaxY = Math.Max(MaxY, bounds.MaxY);
MaxZ = Math.Max(MaxZ, bounds.MaxZ);
}
public void Intersect(AABB cuttingNodeBounds,
Plane[] cuttingNodePlanes,
Vector3 cuttingNodeTranslation,
Vector3 inputPolygonTranslation,
List<Polygon> inputPolygons,
List<Polygon> inside,
List<Polygon> aligned,
List<Polygon> revAligned,
List<Polygon> outside)
{
var categories = new PolygonSplitResult[cuttingNodePlanes.Length];
var translatedPlanes = new Plane[cuttingNodePlanes.Length];
var translation = Vector3.Subtract(cuttingNodeTranslation, inputPolygonTranslation);
// translate the planes we cut our polygons with so that they're located at the same
// relative distance from the polygons as the brushes are from each other.
for (int i = 0; i < cuttingNodePlanes.Length; i++)
translatedPlanes[i] = Plane.Translated(cuttingNodePlanes[i], translation);
var vertices = this.Vertices;
var edges = this.Edges;
var planes = this.Planes;
for (int i = inputPolygons.Count - 1; i >= 0; i--)
{
var inputPolygon = inputPolygons[i];
if (inputPolygon.FirstIndex == -1)
continue;
var bounds = inputPolygon.Bounds;
var finalResult = PolygonSplitResult.CompletelyInside;
// A quick check if the polygon lies outside the planes we're cutting our polygons with.
if (!AABB.IsOutside(cuttingNodeBounds, translation, bounds))
{
PolygonSplitResult intermediateResult;
Polygon outsidePolygon = null;
for (int otherIndex = 0; otherIndex < translatedPlanes.Length; otherIndex++)
{
var translatedCuttingPlane = translatedPlanes[otherIndex];
var side = cuttingNodePlanes[otherIndex].OnSide(bounds, -translation);
if (side == PlaneSideResult.Outside)
{
finalResult = PolygonSplitResult.CompletelyOutside;
break; // nothing left to process, so we exit
} else
if (side == PlaneSideResult.Inside)
continue;
var polygon = inputPolygon;
intermediateResult = PolygonSplit(translatedCuttingPlane, inputPolygonTranslation, ref polygon, out outsidePolygon);
inputPolygon = polygon;
if (intermediateResult == PolygonSplitResult.CompletelyOutside)
{
finalResult = PolygonSplitResult.CompletelyOutside;
break; // nothing left to process, so we exit
} else
if (intermediateResult == PolygonSplitResult.Split)
{
if (outside != null)
outside.Add(outsidePolygon);
// Note: left over is still completely inside,
// or plane (opposite) aligned
} else
if (intermediateResult != PolygonSplitResult.CompletelyInside)
finalResult = intermediateResult;
}
} else
finalResult = PolygonSplitResult.CompletelyOutside;
switch (finalResult)
{
case PolygonSplitResult.CompletelyInside: inside .Add(inputPolygon); break;
case PolygonSplitResult.CompletelyOutside: outside.Add(inputPolygon); break;
// The polygon can only be visible if it's part of the last brush that shares it's surface area,
// otherwise we'd get overlapping polygons if two brushes overlap.
// When the (final) polygon is aligned with one of the cutting planes, we know it lies on the surface of
// the CSG node we're cutting the polygons with. We also know that this node is not the node this polygon belongs to
// because we've done that check earlier on. So we flag this polygon as being invisible.
case PolygonSplitResult.PlaneAligned: inputPolygon.Visible = false; aligned .Add(inputPolygon); break;
case PolygonSplitResult.PlaneOppositeAligned: inputPolygon.Visible = false; revAligned.Add(inputPolygon); break;
}
}
}
public static CSGMesh Combine(Vector3 offset, IDictionary<CSGNode, CSGMesh> brushMeshes)
{
var planeLookup = new Dictionary<Plane, short>();
var vertexLookup = new Dictionary<Vector3, short>();
var planes = new List<Plane>();
var polygons = new List<Polygon>();
var edges = new List<HalfEdge>();
var vertices = new List<Vector3>();
var bounds = new AABB();
bounds.Clear();
int edgeIndex = 0;
int polygonIndex = 0;
foreach (var item in brushMeshes)
{
var node = item.Key;
var translation = Vector3.Subtract(node.Translation, offset);
var mesh = item.Value;
foreach (var edge in mesh.Edges)
{
short vertexIndex;
var vertex = Vector3.Add(mesh.Vertices[edge.VertexIndex], translation);
if (!vertexLookup.TryGetValue(vertex, out vertexIndex))
{
vertexIndex = (short)vertices.Count;
vertices.Add(vertex);
vertexLookup.Add(vertex, vertexIndex);
}
var newEdge = new HalfEdge();
newEdge.VertexIndex = vertexIndex;
newEdge.NextIndex = (short)(edge.NextIndex + edgeIndex);
newEdge.TwinIndex = (short)(edge.TwinIndex + edgeIndex);
newEdge.PolygonIndex = (short)(edge.PolygonIndex + polygonIndex);
edges.Add(newEdge);
}
foreach (var polygon in mesh.Polygons)
{
if (polygon.FirstIndex == -1)
continue;
short planeIndex;
var plane = mesh.Planes[polygon.PlaneIndex];
if (!planeLookup.TryGetValue(plane, out planeIndex))
{
planeIndex = (short)planes.Count;
planes.Add(plane);
planeLookup.Add(plane, planeIndex);
}
var newPolygon = new Polygon();
newPolygon.PlaneIndex = planeIndex;
newPolygon.FirstIndex = (short)(polygon.FirstIndex + edgeIndex);
newPolygon.Category = polygon.Category;
newPolygon.Visible = polygon.Visible;
newPolygon.Bounds.Set(polygon.Bounds, translation);
polygons.Add(newPolygon);
if (newPolygon.Visible)
{
var first = edges[newPolygon.FirstIndex];
var iterator = first;
do
{
bounds.Add(vertices[iterator.VertexIndex]);
iterator = edges[iterator.NextIndex];
} while (iterator != first);
}
}
edgeIndex = edges.Count;
polygonIndex = polygons.Count;
}
return new CSGMesh(planes.ToArray(), polygons, edges, vertices, bounds);
}
public CSGMesh Clone()
{
var newPlanes = new Plane[Planes.Length];
for (int i = 0; i < Planes.Length; i++)
{
var plane = Planes[i];
newPlanes[i] = new Plane(plane.A, plane.B, plane.C, plane.D);
}
var newPolygons = new List<Polygon>(Polygons.Count);
foreach (var polygon in Polygons)
{
var newPolygon = new Polygon();
newPolygon.FirstIndex = polygon.FirstIndex;
newPolygon.Visible = polygon.Visible;
newPolygon.Category = polygon.Category;
newPolygon.PlaneIndex = polygon.PlaneIndex;
newPolygon.Bounds.Set(polygon.Bounds);
newPolygons.Add(newPolygon);
}
var newEdges = new List<HalfEdge>(Edges.Count);
foreach (var edge in Edges)
{
var newEdge = new HalfEdge();
newEdge.NextIndex = edge.NextIndex;
newEdge.PolygonIndex = edge.PolygonIndex;
newEdge.TwinIndex = edge.TwinIndex;
newEdge.VertexIndex = edge.VertexIndex;
newEdges.Add(newEdge);
}
var newVertices = new List<Vector3>(Vertices.Count);
foreach (var vertex in Vertices)
{
var newVertex = new Vector3();
newVertex.X = vertex.X;
newVertex.Y = vertex.Y;
newVertex.Z = vertex.Z;
newVertices.Add(newVertex);
}
var newBounds = new AABB(Bounds);
var newMesh = new CSGMesh(
newPlanes,
newPolygons,
newEdges,
newVertices,
newBounds);
return newMesh;
}
public static CSGMesh CreateFromPlanes(Plane[] brushPlanes)
{
var planes = new Plane[brushPlanes.Length];
for (int i = 0; i < brushPlanes.Length; i++)
{
var plane = brushPlanes[i];
planes[i] = new Plane(plane.A, plane.B, plane.C, plane.D);
}
var pointIntersections = new List<PointIntersection>(planes.Length * planes.Length);
var intersectingPlanes = new List<short>();
var vertices = new List<Vector3>();
var edges = new List<HalfEdge>();
// Find all point intersections where 3 (or more planes) intersect
for (short planeIndex1 = 0; planeIndex1 < planes.Length - 2; planeIndex1++)
{
var plane1 = planes[planeIndex1];
for (short planeIndex2 = (short)(planeIndex1 + 1); planeIndex2 < planes.Length - 1; planeIndex2++)
{
var plane2 = planes[planeIndex2];
for (short planeIndex3 = (short)(planeIndex2 + 1); planeIndex3 < planes.Length; planeIndex3++)
{
var plane3 = planes[planeIndex3];
// Calculate the intersection
var vertex = Plane.Intersection(plane1, plane2, plane3);
// Check if the intersection is valid
if (float.IsNaN(vertex.X) || float.IsNaN(vertex.Y) || float.IsNaN(vertex.Z) ||
float.IsInfinity(vertex.X) || float.IsInfinity(vertex.Y) || float.IsInfinity(vertex.Z))
continue;
intersectingPlanes.Clear();
intersectingPlanes.Add(planeIndex1);
intersectingPlanes.Add(planeIndex2);
intersectingPlanes.Add(planeIndex3);
for (short planeIndex4 = 0; planeIndex4 < planes.Length; planeIndex4++)
{
if (planeIndex4 == planeIndex1 ||
planeIndex4 == planeIndex2 ||
planeIndex4 == planeIndex3)
continue;
var plane4 = planes[planeIndex4];
var side = plane4.OnSide(vertex);
if (side == PlaneSideResult.Intersects)
{
if (planeIndex4 < planeIndex3)
// Already found this vertex
goto SkipIntersection;
// We've found another plane which goes trough our found intersection point
intersectingPlanes.Add(planeIndex4);
}
else
if (side == PlaneSideResult.Outside)
// Intersection is outside of brush
goto SkipIntersection;
}
var vertexIndex = (short)vertices.Count;
vertices.Add(vertex);
// Add intersection point to our list
pointIntersections.Add(new PointIntersection(vertexIndex, intersectingPlanes));
SkipIntersection:
;
}
}
}
var foundPlanes = new short[2];
// Find all our intersection edges which are formed by a pair of planes
// (this could probably be done inside the previous loop)
for (int i = 0; i < pointIntersections.Count; i++)
{
var pointIntersectionA = pointIntersections[i];
for (int j = i + 1; j < pointIntersections.Count; j++)
{
var pointIntersectionB = pointIntersections[j];
var planesIndicesA = pointIntersectionA.PlaneIndices;
var planesIndicesB = pointIntersectionB.PlaneIndices;
short foundPlaneIndex = 0;
foreach (var currentPlaneIndex in planesIndicesA)
{
if (!planesIndicesB.Contains(currentPlaneIndex))
continue;
foundPlanes[foundPlaneIndex] = currentPlaneIndex;
foundPlaneIndex++;
if (foundPlaneIndex == 2)
break;
}
// If foundPlaneIndex is 0 or 1 then either this combination does not exist,
// or only goes trough one point
if (foundPlaneIndex < 2)
continue;
// Create our found intersection edge
var halfEdgeA = new HalfEdge();
var halfEdgeAIndex = (short)edges.Count;
edges.Add(halfEdgeA);
var halfEdgeB = new HalfEdge();
var halfEdgeBIndex = (short)edges.Count;
edges.Add(halfEdgeB);
halfEdgeA.TwinIndex = halfEdgeBIndex;
halfEdgeB.TwinIndex = halfEdgeAIndex;
halfEdgeA.VertexIndex = pointIntersectionA.VertexIndex;
halfEdgeB.VertexIndex = pointIntersectionB.VertexIndex;
// Add it to our points
pointIntersectionA.Edges.Add(new EdgeIntersection(
halfEdgeA,
foundPlanes[0],
foundPlanes[1]));
pointIntersectionB.Edges.Add(new EdgeIntersection(
halfEdgeB,
foundPlanes[0],
foundPlanes[1]));
}
}
var polygons = new List<Polygon>();
for (short i = 0; i < (short)planes.Length; i++)
{
var polygon = new Polygon();
polygon.PlaneIndex = i;
polygons.Add(polygon);
}
var bounds = new AABB();
var direction = new Vector3();
for (int i = pointIntersections.Count - 1; i >= 0; i--)
{
var pointIntersection = pointIntersections[i];
var pointEdges = pointIntersection.Edges;
// Make sure that we have at least 2 edges ...
// This may happen when a plane only intersects at a single edge.
if (pointEdges.Count <= 2)
{
pointIntersections.RemoveAt(i);
continue;
}
var vertexIndex = pointIntersection.VertexIndex;
var vertex = vertices[vertexIndex];
for (int j = 0; j < pointEdges.Count - 1; j++)
{
var edge1 = pointEdges[j];
for (int k = j + 1; k < pointEdges.Count; k++)
{
var edge2 = pointEdges[k];
int planeIndex1 = -1;
int planeIndex2 = -1;
// Determine if and which of our 2 planes are identical
if (edge1.PlaneIndices[0] == edge2.PlaneIndices[0]) { planeIndex1 = 0; planeIndex2 = 0; }
else
if (edge1.PlaneIndices[0] == edge2.PlaneIndices[1]) { planeIndex1 = 0; planeIndex2 = 1; }
else
if (edge1.PlaneIndices[1] == edge2.PlaneIndices[0]) { planeIndex1 = 1; planeIndex2 = 0; }
else
if (edge1.PlaneIndices[1] == edge2.PlaneIndices[1]) { planeIndex1 = 1; planeIndex2 = 1; }
else
continue;
HalfEdge ingoing;
HalfEdge outgoing;
short outgoingIndex;
var shared_plane = planes[edge1.PlaneIndices[planeIndex1]];
var edge1_plane = planes[edge1.PlaneIndices[1 - planeIndex1]];
var edge2_plane = planes[edge2.PlaneIndices[1 - planeIndex2]];
direction = Vector3.Cross(shared_plane.Normal, edge1_plane.Normal);
// Determine the orientation of our two edges to determine
// which edge is in-going, and which one is out-going
if (Vector3.Dot(direction, edge2_plane.Normal) < 0)
{
ingoing = edge2.Edge;
outgoingIndex = edge1.Edge.TwinIndex;
outgoing = edges[outgoingIndex];
}
else
{
ingoing = edge1.Edge;
outgoingIndex = edge2.Edge.TwinIndex;
outgoing = edges[outgoingIndex];
}
// Link the out-going half-edge to the in-going half-edge
ingoing.NextIndex = outgoingIndex;
// Add reference to polygon to half-edge, and make sure our
// polygon has a reference to a half-edge
// Since a half-edge, in this case, serves as a circular
// linked list this just works.
var polygonIndex = edge1.PlaneIndices[planeIndex1];
ingoing.PolygonIndex = polygonIndex;
outgoing.PolygonIndex = polygonIndex;
var polygon = polygons[polygonIndex];
polygon.FirstIndex = outgoingIndex;
polygon.Bounds.Add(vertex);
}
}
// Add the intersection point to the area of our bounding box
bounds.Add(vertex);
}
return new CSGMesh(planes, polygons, edges, vertices, bounds);
}